Using ArcGIS, there are two general methods for subsetting a shapefile. If you have features within your counties .shp (e.g. administrative voting areas, census zones etc), simply select those feature and export them as a new shapefile (Figure 1).

The second method involves clipping a subset of your county .shp based on a polygon. You can accomplish this using the Clip tool.

You can import it in qgis. Then you can select that specific area using query on data in the attribute table and then when you got that area right click on your existing layer-->save selection as and then save that new vector layer as new shp file. I hope it works.